Question

choose the correct values for x and y in the right triangle. y = 6√2 y = 6 x = 3 x = 3√2

Explanation:

Step1: Identify triangle type

This is a 45 - 45-90 right - triangle. In a 45 - 45-90 right - triangle, the legs are equal and the hypotenuse $y$ is $\sqrt{2}$ times the length of a leg $x$. Let the length of one leg be $x$, and the other leg is also $x$ (since the non - right angles are 45 degrees each), and the hypotenuse is $y$. Given one leg is $3\sqrt{2}$.

Step2: Find the value of $x$

Since the legs of a 45 - 45-90 triangle are equal, if one leg is $3\sqrt{2}$, then $x = 3\sqrt{2}$.

Step3: Find the value of $y$

The relationship between the leg $x$ and hypotenuse $y$ in a 45 - 45-90 triangle is $y=\sqrt{2}x$. Substitute $x = 3\sqrt{2}$ into the formula: $y=\sqrt{2}\times3\sqrt{2}=3\times2 = 6$.

Answer:

$x = 3\sqrt{2}$, $y = 6$